Higher order selfdual toric varieties

The notion of higher order dual varieties of a projective variety, introduced in Piene [Singularities, part 2, (Arcata, Calif., 1981), Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, 1983 ], is a natural generalization of the classical notion of projective dua...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 196; no. 5; pp. 1759 - 1777
Main Authors Dickenstein, Alicia, Piene, Ragni
Format Journal Article
LanguageEnglish
Norwegian
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017
Springer Nature B.V
Springer Berlin/Heidelberg
Subjects
Combinatorial analysis
Mathematics
Mathematics and Statistics
Singularity (mathematics)
Higher Order Duality
Interior Lattice Points
Toric Varieties
Cayley-Bacharach Theorem
Torus Embedding
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Summary:The notion of higher order dual varieties of a projective variety, introduced in Piene [Singularities, part 2, (Arcata, Calif., 1981), Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, 1983 ], is a natural generalization of the classical notion of projective duality. In this paper, we present geometric and combinatorial characterizations of those equivariant projective toric embeddings that satisfy higher order selfduality. We also give several examples and general constructions. In particular, we highlight the relation with Cayley–Bacharach questions and with Cayley configurations.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-017-0637-4